Atomic scale reordering of lattices can induce local modulations of functional material properties, such as reflectance and ferromagnetism. Pulsed femtosecond laser irradiation enables lattice reordering in the picosecond range. However, the dependence of the phase transitions on the initial lattice order as well as the temporal dynamics of these transitions remain to be understood. This study investigates the laser-induced atomic reordering and the concomitant onset of ferromagnetism in thin Fe-based alloy films with vastly differing initial atomic orders. The optical response to single femtosecond laser pulses on selected prototype systems, one that initially possesses positional disorder, Fe₆₀V₄₀, and a second system initially in a chemically ordered state, Fe₆₀Al₄₀, has been tracked with time. Despite the vastly different initial atomic orders the structure in both systems converges to a positionally ordered but chemically disordered state, accompanied by the onset of ferromagnetism. Time-resolved measurements of the transient reflectance combined with simulations of the electron and phonon temperatures reveal that the reordering processes occur via the formation of a transient molten state with an approximate lifetime of 200 ps. These findings provide insights into the fundamental processes involved in laser-induced atomic reordering, paving the way for controlling material properties in the picosecond range.